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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Finding a "special" non singular submatrix
Given a square integer matrix $A \in M_n(Z)$ and two subsets $I, J \subset \{ 1, \ldots, n\}$, we define $A_{I,J}$ as the sub-matrix of $A$ containing the rows (resp. columns) whose index is in $I$ (r …
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How many simplicial complexes on n vertices up to homotopy equivalence?
The sequence A261005 of OEIS should be helpful, since it is an upper bound. However, I don't know any closed formula for the number of simplicial complexes on n unlabeled vertices (without the homotop …